Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
Bibliographic record
Abstract
Given a state of light, how do its properties change when only some of the constituent photons are observed and the rest are neglected (traced out)? By developing formulas for mode-agnostic removal of photons from a beam, we show how the expectation value of any operator changes when only q photons are inspected from a beam, ignoring the rest. We use this to re-express expectation values of operators in terms of the state obtained by randomly selecting q photons. Remarkably, this only equals the true expectation value for a unique value of q: expressing the operator as a monomial in normally ordered form, q must be equal to the number of photons annihilated by the operator. A useful corollary is that the coefficients of any q-photon state chosen at random from an arbitrary state are exactly the qth-order correlations of the original state; one can inspect the intensity moments to learn what any random photon will be doing and, conversely, one need only look at the n-photon subspace to discern what all of the nth-order correlation functions are. The astute reader will be pleased to find no surprises here, only mathematical justification for intuition. Our results hold for any completely symmetric state of any type of particle with any combination of numbers of particles and can be used wherever bosonic correlations are found.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".